Minor SQL-database repair, SEO and webshop upgrade

Tarjouspyynnön kuvaus

My Wordpress website with basic webshop has been up and running, but I would now need help with three quite unrelated aspects:
***the first one is urgent, the others not that much. So if you only want to do the first point, that's ok***
1) the size of the SQL-database has gone over a critical limit, I can't login anymore on Wordpress. My server provides possibility for a database with larger critical limit, but I don't know how to transfer the thing. Also this would be a good occasion to clean up the database.
2) This is anyway related to the first point: what else than cleaning the database can we do to speed up the website and make it otherwise better from SEO perspective?
3) My Woocommerce-based webshop works to some degree, and it's directly connected to the database of my shop software. I would like to add some standard functionalities such as filter by brand, order by price etc. I would also like to have the webshop more integrated onto web pages, so that for example my page about Brand X also has products of Brand X there.
4) In a later stage I would definitely like a 'facelift' of the current website to make it look more professional. That doesn't need to be now but feel free to make an offer.